The conceptual significance of the quantum SWITCH has been questioned by physicists working on the causal modelling approach. In particular, in ref [1]} MacLean et al make two objections to the claim that the quantum SWITCH represents a genuine superposition of two different causal orders. The first is that the two branches do not really contain copies of the same events in different orders; the events occur at different times in each of the branches, so really we should think of them as completely distinct events. Guérin and Brukner[2]} respond to this by invoking diffeomorphism invariance to argue that events cannot be identified across branches by their spacetime location, since that is not a diffeomorphism-invariant fact - instead they must be identified by the intrinsic properties of the event, which are the same in each branch of the quantum SWITCH. Now, this argument might succeed if it these events were occurring in complete isolation so that there were no way to identify them other than either spacetime location or the intrinsic properties of the event. But in this case the events are not isolated: they are controlled by an external system and thus they stand in well-defined relations to that external system, meaning that there are many ways they can be identified by means of their relations to other external events. Diffeomorphism invariance is thus not really a relevant consideration in this kind of experiment.
